Flying into Pisa

At Pisa airport, you take the new people-mover tram directly to Pisa Centrale station and get a train there to Firenze S.M. Novella station. Fare is 11.10 EUR including the people-mover and you buy a ticket out of a vending machine and validate it before boarding in the stamping machine on the platform. Connections every 30 minutes in the afternoon.

I've done it the other way: Florence to the Pisa airport. It's very easy and Sam has given you very good instructions.

I will add that we've taken a very nice coach bus non-stop from S.M. Novella to the Pisa airport, and from there we took a People Mover bus to Pisa Centrale (the new PM tram was still under construction). We were dealing with a train strike and it was our best option at the time! Anyway, if you are interested in the bus - which runs about every 45 minutes, takes about an hour, and costs about 12,00 euro - here's the weblink:

http://www.pisa-airport.com/en/the-passengers/transport/bus.html

https://www.airportbusexpress.it

If nothing else, I thought I'd throw it out for anyone who might need an alternative to the train. It's also nice if you want to go directly to/from the airport to/from Florence as you can bypass Centrale. We bought our tickets same day.

In addition to the peoplemover + train to Florence you can also take the airport shuttle bus, which in my opinion, is more convenient and takes the same amount of time as the train.
Check if times work for you. Two bus companies to choose from.
https://www.airportbusexpress.it
http://www.caronnatour.com/new-direct-sky-bus-lines-en/

Pisa airport is great, nice and small!
Type of place where you have to walk down the steps from the plane to the ground and then walk into the terminal where your bags are.
No worries about lines!

I flew in and then took a private driver ride to Florence with a stop off at the Pisa Tower in-route (even though not really in-route but I paid extra to have them stop here and wait for us). I thought the drive after a long flight was a good value plus allowed us to see the Tower area for 45 minutes or so. For a party of 1 though it probably does not make sense.
You could still work in a stop here if taking the train, I am certain I have read there is bag storage rental available at the Pisa station.

A big thank you to everyone for your help! I booked my flight into Pisa and I could not be more excited!
Now I have three full days in Florence to plan prior to my friends arriving!
Thanks again!
Lisa

I see you've already booked your flight, so this is more reassurance than anything, but yes! The Pisa airport is actually much bigger than Florence (counter to what most would think based on city size). Easy journey into Florence SMN (train or bus station) and you'll be right in the center of the city. Buon viaggio :)

Thanks, bedofstars! Always good to have a little reassurance after a major purchase like an airline ticket. :)